On the general Sombor index of unicyclic graphs with a given diameter

Xipeng Hu; Lingping Zhong

On the general Sombor index of unicyclic graphs with a given diameter

Combinatorics 2022-08-02 v1

Authors: Xipeng Hu , Lingping Zhong

Abstract

The general Sombor index of $G$ is defined as $SO_{\alpha}(G)= \sum_{uv\in G}\left(d^2_{G}(u)+d^2_{G}(v)\right)^{\alpha}$ . For $0<\alpha<1$ , we have the upper bound of $SO_{\alpha}(G)$ on unicyclic graphs with a fixed diameter, and the extremal graph is also characterized.

Keywords

general sombor index unicyclic graphs diameter upper bound extremal graph

Cite

@article{arxiv.2208.00418,
  title  = {On the general Sombor index of unicyclic graphs with a given diameter},
  author = {Xipeng Hu and Lingping Zhong},
  journal= {arXiv preprint arXiv:2208.00418},
  year   = {2022}
}

Comments

12 pages, 5 figures

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